# Valuation of contingent convertible catastrophe bonds — The case for equity conversion

*Krzysztof Burnecki*,
*Mario Nicoló Giuricich* and
*Zbigniew Palmowski*

*Insurance: Mathematics and Economics*, 2019, vol. 88, issue C, 238-254

**Abstract:**
Within the context of banking-related literature on contingent convertible bonds, we comprehensively formalise the design and features of a relatively new type of insurance-linked security, called a contingent convertible catastrophe bond (CocoCat). We begin with a discussion on its design and compare its relative merits to catastrophe bonds and catastrophe-equity puts. Subsequently, we derive analytical valuation formulae for index-linked CocoCats under the assumption of independence between natural catastrophe and financial market risks. We model natural catastrophe losses by a time-inhomogeneous compound Poisson process, with the interest-rate process governed by the Longstaff model. By using an exponential change of measure on the loss process, as well as a Girsanov-like transformation to synthetically remove the correlation between the share and interest-rate processes, we obtain these analytical formulae. Using selected parameter values in line with earlier research, we numerically analyse our valuation formulae for index-linked CocoCats. An analysis of the results reveals that the CocoCat prices are most sensitive to changing interest-rates, conversion fractions and the threshold levels defining the trigger times.

**Keywords:** Catastrophe risk; Contingent convertible bond; Time-inhomogeneous compound Poisson process; Longstaff model; Risk neutral measure; Heavy-tailed data (search for similar items in EconPapers)

**Date:** 2019

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Working Paper: Valuation of contingent convertible catastrophe bonds - the case for equity conversion (2018)

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**Persistent link:** https://EconPapers.repec.org/RePEc:eee:insuma:v:88:y:2019:i:c:p:238-254

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